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There is a whole lot more to it than points, the idea is a "balance" of some type.

I like going to this little publication when thinking it through:
https://static1.squarespace.com/static/50f14d35e4b0d70ab5fc4f24/t/53ef1dbae4b0a6d424125a6f/1408179642248/GDC+2009+sirlin+handout6.pdf

Points would be utterly determined by how "powerful" the unit is able to be within the game structure.
Again, some mechanisms built into the rules can help eliminate what was intended as a "perk" to an out and out overpowered ability.
http://www.sirlin.net/articles/balancing-multiplayer-games-part-3-fairness

I am a big fan of Sirlin, tends to be controversial due to the "Playing to Win" publication.
We tend to get a bit too abstract while this guy breaks it down into parts.

Any game that allows the players to choose what forces they will deploy and in what strength must have some kind of points system for quantifying the relative power of those forces. Usually this will be for making a balanced match but also for allowing a quantified handicap system. Chess doesn't have a points system but chess doesn't let you choose your forces.

Force composition is as much part of the game as the actual game level manoeuvre for wargames, consequently some kind of points system is virtually mandatory. The more game elements the more the complexity of the game will make a points system incapable of truly representing the power of the unit in question not least because that power depends a lot on a specific context. What is an anti-tank gun worth? In the context of an enemy army fielding swarms of unarmoured infantry not much but it is worth a lot in a context where the enemy army will be a few highly armoured high value targets. What is the value of the ability to gain double cover from wooded terrain? A lot in on heavily wooded terrain but nothing on a open desert battlefield. And so it goes. Even the most rigorously tested and evaluated points system will be rendered inaccurate by specific contexts at the very least but they remain mandatory all the same.

 Easy E wrote:
For many years, pre-made army lists based on historical research and precedent was enough. So this "Points" thing is the newer phenomenon and probably speaks to the state of "modern" wargaming rather than anything inherent in wargaming itself.

Indeed it is.

Also, the "Old Guard" of the 50s and 60s were concerned only with historical wargaming, not hypotheticals such as fantasy or Sci-Fi for which we have no real world reference. For example, "Heavy Infantry" regardless of nationality would be considered equivalent within that time period. They were not usually concerned with details such as the possible superiority of the Pre-Marian Roman Legion over the Successor era Macedonian Phalanx. If such a thing were the crux of a scenario (e.g. Battle of Cynoscephalae itself), they would probably add a special rule for that day's game only, not an overarching one.

For example, I include a partially transcribed scenario from the book Scenarios for Wargames ( Wargame Research Group 1981) by Charles Stewart Grant, one of the early pioneers of miniature gaming.

EDIT: Please pardon my mistake. I've mixed up Mr. Grant with Brigadier Peter Young. Both were involved in early wargaming, but if Mr. Grant was a WWII veteran like Brigadier Young my book does not say.

*****
Rear Slope

There is a simple map showing a large but gently sloping hill with a small woods on the defender's right flank. To the west of the wood is a road running North-South. On the defender's left the hill ends in a small farm. The introduction discusses how most major defensive battles have been with all the defensive forces exposed to the attacker's recon (and artillery), but the use of the "rear slope" negates that. Mr. Grant mentions that the scenario that follows can be played in any time period, but is most applicable for the horse and musket period. (The most famous and decisive use of the rear slope was the Battle of Waterloo, 18 June 1815.)

Mr. Grant then lists mission objectives and "force lists" for each side, with Blue the defender and Red the attacker.

Blue Force: Mission Objective. Hold the hill feature to the east of the road. Forces: 4 units of infantry, 1 unit of light infantry, 2 units of heavy cavalry, 4 guns. Execution: The Blue force commander must deploy four units forward of the line x-y (shown on the map) in his initial deployment. The remainder are concealed (marked on a map). Movement over the crest in either direction is permitted once the game starts.

Red Force: Mission Objective. Seize the hill feature to the east of the road. Forces: 7 units of infantry, 1 unit of light infantry, 1 unit of light cavalry, 2 units of heavy cavalry, 4 guns. Execution: The Red force commander has reconnoitred the battlefield and has seen what is to be seen of the enemy position. He is able to enter the battlefield between points A and B (essentially 80% of his table edge excluding the western portion where the road runs off the southern part of the map).
*****
With the increased granularity of point-based systems, and especially fantasy/sci-fi ones, the above scenario would be wildly unbalanced if we just used the unit equivalency listed above. Using 5th edition WHFB (which is when I last played) I am confident that if Blue was Dwarves and Red just pure Goblins that Red will be routed in short order. We'd have to give the gobbos more than just 7 units of basic infantry to make up the difference in quality.

TL: DR. Early wargaming tried to balance scenarios not by points, but by initial set up and force list, and assuming all forces in a given time period were of the same fighting quality regardless of nationality.